[Case Study]Mining Association Rules using R

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Authors:	Michael Hahsler, Bettina Grün, Kurt Hornik
Title:	[download] (15527)arules - A Computational Environment for Mining Association Rules and Frequent Item Sets
Reference:	Vol. 14, Issue 15, Sep 2005Submitted 2005-04-15, Accepted 2005-09-29
Type:	Article
Abstract:	Mining frequent itemsets and association rules is a popular and well researched approach for discovering interesting relationships between variables in large databases. The R package arules presented in this paper provides a basic infrastructure for creating and manipulating input data sets and for analyzing the resulting itemsets and rules. The package also includes interfaces to two fast mining algorithms, the popular C implementations of Apriori and Eclat by Christian Borgelt. These algorithms can be used to mine frequent itemsets, maximal frequent itemsets, closed frequent itemsets and association rules.

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关键词：Association Case study Using Rules ATION databases presented provides Michael between

Example 1: Analyzing and preparing a transaction data set

In this example, we show how a data set can be analyzed and manipulated before associations are mined. This is important for finding problems in the data set which could make the mined associations useless or at least inferior to associations mined on a properly prepared data set.
For the example, we look at the Epub transaction data contained in package arules. This data set contains downloads of documents from the Electronic Publication platform of the Vienna University of Economics and Business available via http://epub.wu-wien.ac.at from January 2003 to December 2008.

1. library("arules")
   
2. data("Epub")
   
3. Epub
   
4. 
   
5. summary(Epub)
   
6. year <- strftime(as.POSIXlt(transactionInfo(Epub)[["TimeStamp"]]), "%Y")
   
7. table(year)
   
8. 
   
9. Epub2003 <- Epub[year == "2003"]
   
10. length(Epub2003)
    
11. image(Epub2003)
    
12. transactionInfo(Epub2003[size(Epub2003)  20])
    
13. inspect(Epub2003[1:5])
    
14. 
    
15. as(Epub2003[1:5], "list")
    
16. EpubTidLists <- as(Epub, "tidLists")
    
17. EpubTidLists
    
18. 
    
19. as(EpubTidLists[1:3], "list")

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Example 2: Preparing and mining a questionnaire data set

As a second example, we prepare and mine questionnaire data. We use the Adult data set from the UCI machine learning repository (Asuncion and Newman 2007) provided by package arules. This data set is similar to the marketing data set used by Hastie et al. (2001) in their chapter about association rule mining. The data originates from the U.S. census bureau database and contains 48842 instances with 14 attributes like age, work class, education, etc. In the original applications of the data, the attributes were used to predict the income level of individuals. We added the attribute income with levels small and large,
representing an income of ≤ USD 50,000 and > USD 50,000, respectively. This data is included in arules as the data set AdultUCI.

1. data("AdultUCI")
   
2. dim(AdultUCI)
   
3. AdultUCI[1:2,]
   
4. 
   
5. AdultUCI[["fnlwgt"]] <- NULL
   
6. AdultUCI[["education-num"]] <- NULL
   
7. AdultUCI[[ "age"]] <- ordered(cut(AdultUCI[[ "age"]], c(15,25,45,65,100)),
   
8. + labels = c("Young", "Middle-aged", "Senior", "Old"))
   
9. AdultUCI[[ "hours-per-week"]] <- ordered(cut(AdultUCI[[ "hours-per-week"]],
   
10. + c(0,25,40,60,168)),
    
11. + labels = c("Part-time", "Full-time", "Over-time", "Workaholic"))
    
12. AdultUCI[[ "capital-gain"]] <- ordered(cut(AdultUCI[[ "capital-gain"]],
    
13. + c(-Inf,0,median(AdultUCI[[ "capital-gain"]][AdultUCI[[ "capital-gain"]]0]),Inf)),
    
14. + labels = c("None", "Low", "High"))
    
15. AdultUCI[[ "capital-loss"]] <- ordered(cut(AdultUCI[[ "capital-loss"]],
    
16. + c(-Inf,0,
    
17. + median(AdultUCI[[ "capital-loss"]][AdultUCI[[ "capital-loss"]]0]),Inf)),
    
18. + labels = c("none", "low", "high"))
    
19. Adult <- as(AdultUCI, "transactions")
    
20. Adult
    
21. summary(Adult)
    
22. itemFrequencyPlot(Adult, support = 0.1, cex.names=0.8)
    
23. Next, we call the function apriori() to find all rules (the default association type for
    
24. apriori()) with a minimum support of 1% and a confidence of 0.6.
    
25. rules <- apriori(Adult,
    
26. + parameter = list(support = 0.01, confidence = 0.6))
    
27. rules
    
28. summary(rules)
    
29. 
    
30. rulesIncomeSmall <- subset(rules, subset = rhs %in% "income=small" & lift  1.2)
    
31. rulesIncomeLarge <- subset(rules, subset = rhs %in% "income=large" & lift  1.2)
    
32. 
    
33. inspect(head(sort(rulesIncomeSmall, by = "confidence"), n = 3))
    
34. 
    
35. inspect(head(sort(rulesIncomeLarge, by = "confidence"), n = 3))
    
36. 
    
37. write(rulesIncomeSmall, file = "data.csv", sep = ",", col.names = NA)
    
38. write.PMML(rulesIncomeSmall, file = "data.xml")

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Example 3: Extending arules with a new interest measure

1. data("Adult")
   
2. 
   
3. fsets <- eclat(Adult, parameter = list(support = 0.05),control = list(verbose=FALSE))
   
4. 
   
5. #For the denominator of all-confidence we need to find all mined single items and their corresponding
   
6. #support values. In the following we create a named vector where the names are the
   
7. #column numbers of the items and the values are their support.
   
8. 
   
9. singleItems <- fsets[size(items(fsets)) == 1]
   
10. 
    
11. ## Get the col numbers we have support for
    
12. 
    
13. singleSupport <- quality(singleItems)$support
    
14. 
    
15. names(singleSupport) <- unlist(LIST(items(singleItems),decode = FALSE))
    
16. 
    
17. head(singleSupport, n = 5)
    
18. 
    
19. #Next, we can calculate the all-confidence
    
20. 
    
21. itemsetList <- LIST(items(fsets), decode = FALSE)
    
22. 
    
23. allConfidence <- quality(fsets)$support /sapply(itemsetList, function(x)+ max(singleSupport[as.character(x)]))
    
24. 
    
25. quality(fsets) <- cbind(quality(fsets), allConfidence)
    
26. 
    
27. summary(fsets)
    
28. 
    
29. 
    
30. fsetsEducation <- subset(fsets, subset = items %pin% "education")
    
31. 
    
32. inspect(sort(fsetsEducation[size(fsetsEducation)1],by = "allConfidence")[1 : 3])

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Example 4: Sampling

In this example, we show how sampling can be used in arules. We use again the Adult data set.

1. > data("Adult")
   
2. > Adult
   
3. > supp <- 0.05
   
4. > epsilon <- 0.1
   
5. > c <- 0.1
   
6. > n <- -2 * log(c)/ (supp * epsilon^2)
   
7. > n
   
8. > AdultSample <- sample(Adult, n, replace = TRUE)
   
9. 
   
10. > itemFrequencyPlot(AdultSample, population = Adult, support = supp,cex.names = 0.7)
    
11. #Alternatively, a sample can be compared with the population using the lift ratio (with lift
    
12. #= TRUE). The lift ratio for each item i is P(i|sample)/P(i|population) where the probabilities
    
13. #are estimated by the item frequencies. A lift ratio of one indicates that the items occur in the
    
14. #sample in the same proportion as in the population. A lift ratio greater than one indicates
    
15. #that the item is over-represented in the sample and vice versa. With this plot, large relative
    
16. #deviations for less frequent items can be identified visually (see Figure 8).
    
17. > itemFrequencyPlot(AdultSample, population = Adult,support = supp, lift = TRUE,cex.names = 0.9)
    
18. #To compare the speed-up reached by sampling we use the Eclat algorithm to mine frequent
    
19. #itemsets on both, the database and the sample and compare the system time (in seconds)
    
20. #used for mining.
    
21. > time <- system.time(itemsets <- eclat(Adult,parameter = list(support = supp), control = list(verbose = FALSE)))
    
22. > time
    
23. 
    
24. > timeSample <- system.time(itemsetsSample <- eclat(AdultSample,parameter = list(support = supp), control = list(verbose = FALSE)))
    
25. > timeSample
    
26. 
    
27. #The first element of the vector returned by system.time() gives the (user) CPU time needed
    
28. #for the execution of the statement in its argument. Therefore, mining the sample instead of
    
29. #the whole data base results in a speed-up factor of:
    
30. > # speed up
    
31. > time[1] / timeSample[1]
    
32. 
    
33. #To evaluate the accuracy for the itemsets mined from the sample, we analyze the difference between the two sets.
    
34. > itemsets
    
35. 
    
36. > itemsetsSample
    
37. 
    
38. #The two sets have roughly the same size. To check if the sets contain similar itemsets, we
    
39. #match the sets and see what fraction of frequent itemsets found in the database were also
    
40. #found in the sample.
    
41. > match <- match(itemsets, itemsetsSample, nomatch = 0)
    
42. > ## remove no matches
    
43. > sum(match>0) / length(itemsets)
    
44. 
    
45. Almost all frequent itemsets were found using the sample. The summaries of the support
    
46. of the frequent itemsets which were not found in the sample and the itemsets which were
    
47. frequent in the sample although they were infrequent in the database give:
    
48. > summary(quality(itemsets[which(!match)])$support)
    
49. 
    
50. > summary(quality(itemsetsSample[-match])$support)
    
51. 
    
52. 
    
53. #For the frequent itemsets which were found in the database and in the sample, we can calculate
    
54. #accuracy from the the error rate.
    
55. > supportItemsets <- quality(itemsets[which(match > 0)])$support
    
56. > supportSample <- quality(itemsetsSample[match])$support
    
57. > accuracy <- 1 - abs(supportSample - supportItemsets) / supportItemsets
    
58. > summary(accuracy)

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